 
Summary: ResourceBounded Strong Dimension versus
ResourceBounded Category
John M. Hitchcock a
and A. Pavan b,1
aDepartment of Computer Science, University of Wyoming,
jhitchco@cs.uwyo.edu
bDepartment of Computer Science, Iowa State University,
pavan@cs.iastate.edu
Abstract
Classically it is known that any set with packing dimension less than 1 is meager
in the sense of Baire category. We establish a resourcebounded extension: if a class
X has strong dimension less than 1, then X is meager. This has the applica
tions of explaining some of Lutz's simultaneous meager, measure 0 results and
providing a new proof of a Gu's strong dimension result on infinitelyoften classes.
Key words: computational complexity, resourcebounded category,
resourcebounded dimension, resourcebounded measure
1 Introduction
The most common mathematical notions of size and dimension now have
resourcebounded versions that are useful for complexity classes. We use to
denote a resource bound such as p (polynomial time) or pspace (polynomial
